NATIONALS backbencher Andrew Broad has openly accused Prime Minister Malcolm Turnbull of a failure of leadership, in another sign of growing tensions inside the federal Coalition.

The Member for Mallee's attack on the Prime Minister over his handling of same-sex marriage comes as Nationals MPs agitate for a commission of inquiry into the banking sector, a move that would risk destabilising the Turnbull government, which continues to resist the move.

"I had a private conversation with the Prime Minister where I said, 'Have you sat down and got Trevor Evans, Warren Entsch, Dean Smith – people on the "yes" [side] – and put them in the room with Eric Abetz, Andrew Hastie and people on the "no" side? And come up with a piece of legislation that is Coalition legislation?'" he said.

Mr Broad argued a ‘lack of leadership from the Coalition, the executive of the Coalition, and the Prime Minister has let down many Australians’, and said there was disappointment on the backbench.

Coalition MPs have been granted a conscience vote on same-sex marriage after the postal survey returned a ‘yes’ result. The government has no formal position on the private member's bill, but has outlined an expectation that the law be changed by the end of the year.

Mr Broad has stated he would vote in accordance with the decision of his electorate on the same-sex marriage vote.

The amendments put forward by various Coalition MPs – intended to strengthen religious exemptions – were knocked off by a grouping of Labor, Greens, crossbench and Liberal senators.

In September, Mr Turnbull said the legislation would contain protections for religious freedoms but the parliament would be charged with debating and amending it.

"We don't have a majority in the Senate and, in any event, it is a free vote," he said.

Mr Broad's criticism follows a tense day on Tuesday, in which former Nationals leader John Anderson branded senior Liberal cabinet minister Christopher Pyne a hypocrite, and Mr Pyne warned Nationals defying government policy by pushing for a banking inquiry – including leader Barnaby Joyce, who has signalled he is open to the idea – that ‘disunity is death’ and the surest way to lose power at the next election.